Practice problems for these concepts can be found at: Definite Integrals Practice Problems for AP Calculus

In this study guide:

- Definite Integrals Involving Algebraic Functions
- Definite Integrals Involving Absolute Value
- Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions
- Definite Integrals Involving Odd and Even Functions

### Definite Integrals Involving Algebraic Functions

### Example 1

Verify your result with a calculator.

### Example 2

Verify your result with a calculator.

### Example 3

Verify your result with a calculator.

### Definite Integrals Involving Absolute Value

### Example 1

Verify your result with a calculator.

### Example 2

Verify your result with a calculator.

### Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions

### Example 1

Verify your result with a calculator.

### Example 2

Verify your result with a calculator.

### Example 3

Verify your result with a calculator.

### Example 4

Verify your result with a calculator.

### Definite Integrals Involving Odd and Even Functions

If *f* is an even function, that is, *f (–x) = f (x)*, and is continuous on *[–a, a]*, then

If *f* is an odd function, that is, *F (x) = – f (–x)*, and is continuous on [*–a, a*] then

### Example 1

Evaluate

Since

f (x)=cos xis an even function,Verify your result with a calculator.

### Example 2

Evaluate

Since

f (x)=xis an even function, i.e.,^{4}– x^{2}f (–x ) = f (x), thusVerify your result with a calculator.

### Example 3

Evaluate

Since

f (x) = sin xis an odd function, i.e.,f (–x)= – f (x), thusYou can also verify the result with a calculator.

### Example 4

If for all values of *k*, then which of the following could be the graph of f ? See Figure 11.3-1.

Thus *f* is an even function. Choice (C).

Practice problems for these concepts can be found at: Definite Integrals Practice Problems for AP Calculus

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